Tridiagonalization of a Symmetric Dense Matrix on a GPU Cluster

Abstract

Symmetric dense Eigen value problems arise in many scientific and engineering simulations. In this paper, we use GPUs to accelerate its main computational kernel, the tridiagonalization of a dense symmetric matrix on a distributed multicore architecture. We then study the performance of this hybrid message-passing/shared-memory/GPU-computing paradigm on up to 16 compute nodes, each of which consists of 16 Intel Sandy Bridge processors and three NVIDIA GPUs. These studies show that such a hybrid paradigm can exploit the underlying hardware architecture and obtain significant speedups over a flat message-passing paradigm can, and they demonstrate a potential of efficiently solving large-scale Eigen value problems on a GPU cluster. Furthermore, these studies may provide insights on the general effects of such hybrid paradigms on emerging high-performance computers.